Question

problem 5 multiplying a trinomial and a binomial got it? a. what is a simpler form of $(2x^2 - 3x + 1)(x - 3)$? b. reasoning how can you use the distributive property to find the product of a trinomial and a binomial?

Explanation:

Step1: Distribute trinomial over binomial

$2x^2(x-3) - 3x(x-3) + 1(x-3)$

Step2: Expand each term

$2x^3 - 6x^2 - 3x^2 + 9x + x - 3$

Step3: Combine like terms

$2x^3 + (-6x^2-3x^2) + (9x+x) - 3$

Step4: Simplify the expression

$2x^3 - 9x^2 + 10x - 3$

Apply the Distributive Property (also called the FOIL method extended to trinomials) by multiplying each term in the trinomial by each term in the binomial, then combine like terms to simplify the result. Specifically, treat the binomial as a single value, distribute each term of the trinomial to multiply with it, expand all individual products, and then group and add/subtract like terms to get the final simplified product.

Answer:

$2x^3 - 9x^2 + 10x - 3$

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